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Simplifying -0.5x2 + 25x + -105 = 0 Reorder the terms: -105 + 25x + -0.5x2 = 0 Solving -105 + 25x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 210 + -50x + x2 = 0 Move the constant term to the right: Add '-210' to each side of the equation. 210 + -50x + -210 + x2 = 0 + -210 Reorder the terms: 210 + -210 + -50x + x2 = 0 + -210 Combine like terms: 210 + -210 = 0 0 + -50x + x2 = 0 + -210 -50x + x2 = 0 + -210 Combine like terms: 0 + -210 = -210 -50x + x2 = -210 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -210 + 625 Reorder the terms: 625 + -50x + x2 = -210 + 625 Combine like terms: -210 + 625 = 415 625 + -50x + x2 = 415 Factor a perfect square on the left side: (x + -25)(x + -25) = 415 Calculate the square root of the right side: 20.371548787 Break this problem into two subproblems by setting (x + -25) equal to 20.371548787 and -20.371548787.Subproblem 1
x + -25 = 20.371548787 Simplifying x + -25 = 20.371548787 Reorder the terms: -25 + x = 20.371548787 Solving -25 + x = 20.371548787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 20.371548787 + 25 Combine like terms: -25 + 25 = 0 0 + x = 20.371548787 + 25 x = 20.371548787 + 25 Combine like terms: 20.371548787 + 25 = 45.371548787 x = 45.371548787 Simplifying x = 45.371548787Subproblem 2
x + -25 = -20.371548787 Simplifying x + -25 = -20.371548787 Reorder the terms: -25 + x = -20.371548787 Solving -25 + x = -20.371548787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -20.371548787 + 25 Combine like terms: -25 + 25 = 0 0 + x = -20.371548787 + 25 x = -20.371548787 + 25 Combine like terms: -20.371548787 + 25 = 4.628451213 x = 4.628451213 Simplifying x = 4.628451213Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.371548787, 4.628451213}
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